Pairs, sets and sequences in first-order theories

In this paper we study the idea of theories with containers, like sets, pairs, sequences. We provide a modest framework to study such theories. We prove two concrete results. First, we show that first order theories of finite signature that have functional non-surjective ordered pairing are definitionally equivalent to extensions in the same language of the basic theory of non-surjective ordered pairing. Secondly, we show that a firstorder theory of finite signature is sequential (is a theory of sequences) iff it is definitionally equivalent to an extension in the same language of a system of weak set theory called WS. Key words: interpretations, sequential theories, weak set theory, coding MSC2000 codes: 03B30, 03F25, 03F40 1 

• Type: Journal
• Year: 2008
• Where: AML
• Authors: Albert Visser
• Keywords: AML 2008, Modest Framework, Order Theories, Theory